Method and apparatus for extended phase correction in phase sensitive magnetic resonance imaging

ABSTRACT

Methods, apparatuses, systems, and software for extended phase correction in phase sensitive Magnetic Resonance Imaging. A magnetic resonance image or images may be loaded into a memory. Two vector images A and B associated with the loaded image or images may be calculated either explicitly or implicitly so that a vector orientation by one of the two vector images at a pixel is substantially determined by a background or error phase at the pixel, and the vector orientation at the pixel by the other vector image is substantially different from that determined by the background or error phase at the pixel. A sequenced region growing phase correction algorithm may be applied to the vector images A and B to construct a new vector image V so that a vector orientation of V at each pixel is substantially determined by the background or error phase at the pixel. A phase corrected magnetic resonance image or images may be generated using the vector image V, and the phase corrected magnetic resonance image or images may be displayed or archived.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.14/380,972, filed Aug. 26, 2014, which is a national phase applicationunder 35 U.S.C. §371 of International Application No. PCT/US2013/027994,filed Feb. 27, 2013, which claims priority to U.S. Provisional PatentApplication Ser. No. 61/604,413, filed Feb. 28, 2012 the entiredisclosure of each of which is incorporated herein by reference.

BACKGROUND

Field of the Invention

The present invention relates generally to the field of medical imaging.More particularly, embodiments of the invention relate to phasesensitive magnetic resonance imaging (MRI) using an extended phasecorrection algorithm, which among other things can process images withmore flexible phases for successful water and fat imaging.

Description of Related Art

MRI has proven useful in the diagnosis of many diseases such as hepaticsteatosis, cancer, multiple sclerosis, sports related injury, and bonemarrow disorders. MRI provides unique imaging capabilities that are notattainable in any other imaging method. For example, MRI can providedetailed images of soft tissues, abnormal tissues such as tumors, andother structures that cannot be readily imaged using techniques likeX-rays. Further, MRI operates without exposing patients to ionizingradiation experienced in X-rays. For these and other reasons, MRI iscommonly utilized in medical and other fields.

In comparison to other imaging modalities, MRI is unique in that an MRIsignal is represented by a complex number, rather than simply a scalar(such as X-ray attenuation in Computed Tomography). The image value foreach image pixel, therefore, usually includes a magnitude and a phase.Although the phase of an image pixel may carry important information andmay be used in many applications such as chemical shift imaging, thermalimaging, and blood flow quantification, it is usually discarded in astandard image reconstruction process. An underlying reason is that someunwanted background or error phase almost always accompanies the desiredphase.

One application for phase correction of MR images includes inversionrecovery imaging. Inversion recovery (IR) is generally used as amagnetization preparation technique in MRI. In IR imaging, alongitudinal magnetization along a main magnetic field is first rotatedto the opposite direction using a 180 degree radiofrequency (RF) pulse.The inverted magnetization can be recovered by T1 relaxation during aninversion time (TI) between the inversion and the excitation RF pulse.One example application of IR imaging is for suppression of a given typeof tissue with a characteristic T1, such as short-tau inversion recovery(STIR) for fat suppression or fluid-attenuated inversion recovery(FLAIR) for cerebral spinal fluid attenuation. Another exampleapplication of IR imaging is for increased tissue contrast from thedoubling of the dynamic range of the longitudinal magnetization. Thelatter application could be useful for imaging of neonate brains,myocardium at delayed enhancement, or for evaluating pulmonary bloodflow.

The potential for increased tissue contrast by IR imaging, however, isnot always realized because conventional MR image reconstructionpreserves only the magnitude of the MR signals and may actually lead toreduced or even reversed contrast in an IR image.

Phase-sensitive IR (PSIR) image reconstruction, in which unwantedbackground or error phase in an IR image is removed, is a technique thatcan restore the contrast loss or reversal resulting from conventionalmagnitude image reconstruction. One challenge in PSIR imagereconstruction is a phase-correction process to separate the intrinsicsignal phase in the complex image from the background or error phase,which is almost unavoidable in an MR image. Several approaches have beenproposed for PSIR image reconstruction including calibration of thephase errors through acquisition of another image without IR or with IRat different TIs. However, these approaches reduce data acquisitionefficiency. Further, spatial misregistration between the actual andcalibration scans due to patient motion can also be problematic.

An alternative approach for PSIR image reconstruction is to determinethe background or error phase from the IR image itself using variousphase correction algorithms. In general, only the signal phase of aneighbor pixel for overall phase correction is used in many of thesephase correction algorithms. As such, pixels with large phase variation,such as in regions of low signal-to-noise ratio (SNR) or along tissueboundaries may corrupt the phase correction process. In order tominimize the effect, an empirical threshold is usually selected toexclude regions of large phase uncertainty. The actual threshold value,however, can be critical. If the value selected is too small, phasecorrection cannot reach beyond the regions defined by the thresholdvalue and may thus be terminated prematurely. Alternatively, if thevalue selected is too large, errors in phase correction may propagateand even corrupt the rest of the process. In a region growing-basedapproach, for example, the selection of the threshold value togetherwith that of the initial seed and the path of the region growing,determines the quality and the scope of the phase correction. To allowphase correction to proceed beyond local phase fluctuations and to avoidpotential corruption due to phase correction errors, an additional adhoc treatment, such as a “bridge filter” is required. Another limitationof the phase correction algorithms is the global polarity of a PSIRimage, which cannot be unambiguously determined from the phasecorrection process itself. Consequently, images from different componentchannels of a phased array coil cannot be readily combined andinconsistency in display may arise for different images of a multi-sliceacquisition.

Another application where correction of phase errors may be important isthe Dixon chemical shift imaging technique. In MRI, the signal-emittingprotons may resonate at different Larmor frequencies because they havedifferent local molecular environments or chemical shift. The two mostdistinct species found in the human body are water and fat, whose Larmorfrequencies are separated by about 3.5 ppm (parts per million). In manyclinical MRI applications, it is desirable to suppress signals from fatbecause they are usually very bright and obscure lesions. Presently, acommonly used method for fat suppression is chemical shift selectivesaturation (CHESS), which, despite its many advantages, is known to beintrinsically susceptible to both radiofrequency (RF) and magnetic fieldinhomogeneity. Another technique that is sometimes used for fatsuppression is the short tau inversion recovery (STIR), which is basedon the characteristically short T1 relaxation constant for fat, ratherthan on its Larmor frequency. The drawbacks of STIR include reduction inscan efficiency and signal-to-noise ratio as well as potentialalteration to the image contrast.

In U.S. Pat. No. 7,227,359, which is incorporated herein by reference,the present inventor described, among other things, region growing basedphase correction methods for phase sensitive MRI. Potential applicationsfor such methods include a two-point Dixon method for water and fatimaging. In a typical two-point Dixon method, two acquired input imageshave water and fat relative phase angles of approximately 0° (in phase)and approximately 180° (opposed phase), respectively. This restrictionof relative phase angles, in turn, imposes certain restrictions oncorresponding echo times that are used for acquiring input images.

In the article Xiang, Magnetic Resonance in Medicine 56:572-584, 2006,which is incorporated herein by reference, Xiang proposed that it ispossible to do water and fat imaging using two input images acquired atmore flexible echo times (e.g., phases that are not substantially equalto 0° and 180°). In that article, Xiang discussed an iterative phasecorrection method and demonstrated water and fat imaging using an inputimage that is in phase and another input image that has a more flexiblephase. Xiang called the iterative phase correction method RIPE, whichstands for Regional Iterative Phasor Extraction. RIPE fundamentallyrelies on a global convergence of local statistical iterations ofdifferent phasor candidates in different regions of an image. Potentiallimitations of the approach include a requirement for prior imagethresholding to successfully exclude low signal-to-noise regions. TheRIPE approach may also run into difficulties when two input images aresubstantially in-phase and substantially 180° out-of-phase, or whenregions of large artifacts (e.g., near metallic implants) are present tocreate an incorrect initial bias for the phasor iterations. Further, thefat signal is modeled as a single spectral resonance with no attenuationas a function of the echo time in Xiang's 2006 Magnetic Resonance inMedicine 56:572-584 implementation of the RIPE approach for two-pointDixon imaging.

More recently in Eggers et al, abstract, 2010 Annual Scientific Meetingof the International Society of Magnetic Resonance in Medicine, andMagnetic Resonance in Medicine 65(1):96-107, 2011, which areincorporated herein by reference, Eggers et al. reported that by usingthe RIPE method, two input images can both be relaxed to have flexiblephases that are substantially different from in-phase and substantiallydifferent from 180° out-of-phase. Further, the fat signal model isextended to include up to 7 separate spectral resonance peaks, which aredetermined from measurements using magnetic resonance spectroscopy.

The increased flexibility associated with the use of images having echotimes that are more flexible than being substantially in-phase andsubstantially 180° out-of-phase can reduce some restrictions of scanparameters and further improve the scan efficiency for techniques suchas dual-echo acquisition. This flexibility, however, also addsadditional variables and complexity to phase error calculations thatwere not considered in previous algorithms. For example, in theabove-referenced publications both by Xiang and by Eggers et al, theimportant step of phase correction in postprocessing images withflexible echo times has—prior to embodiments of the presentdisclosure—been based on a statistical iterative process that is namedRIPE by Xiang. This process involves empirical image thresholding toexclude low signal-to-noise regions. The process may also run intodifficulties when two input images are substantially in-phase andsubstantially 180° out-of-phase, or when regions of large artifacts(e.g., near metallic implants) are present to create an incorrectinitial bias for the phasor iterations. Furthermore, modeling of the fatsignal by Eggers et al. is based on measurement using magnetic resonancespectroscopy that can only account for limited number of spectral peaksand cannot account for other confounding factors such as magnetic fieldstrength, pulse sequence and scan parameters used, and potentiallydifferent relaxation times for the different spectral peaks. Embodimentsof the present disclosure relate generally to alternativepost-processing strategies for phase sensitive magnetic resonanceimaging. When applied to two point Dixon imaging, certain embodiments ofthe present disclosure use a generalized signal model for fat andfeature a particular type of sequenced region-growing scheme thataccounts for additional complexities, without a need for imagethresholding or a statistical iterative processing. Further, thedisclosed sequenced region growing scheme may naturally encompass inputimages that are acquired substantially in-phase and substantially 180°out-of-phase, and is not affected by the presence of regions with largeimage artifacts. Using this post-processing strategy, successful waterand fat separation can be accomplished with, for example, phantom and invivo images by a 3D dual-echo acquisition with flexible echo times.Post-processing strategies of the present disclosure can also bedirectly applied to other useful applications such as, but not limitedto, phase sensitive inversion recovery image, single point Dixonimaging, and single point silicone-specific imaging. In general,embodiments of this disclosure provide, in part, a new sequenced regiongrowing algorithm that is able to correct background or error phase inacquired magnetic resonance image or images.

Referenced shortcomings of some existing or traditional approaches tophase sensitive MRI are not intended to be exhaustive, but rather areamong many that tend to impair the effectiveness of previously knowntechniques concerning image reconstruction; however, those mentionedhere are sufficient to demonstrate that the methodologies appearing inthe art have not been satisfactory and that a need exists for techniquesdescribed and claimed in this disclosure.

SUMMARY OF THE INVENTION

Certain shortcomings of the prior art may be reduced or eliminated bysome or all of the techniques disclosed here. These techniques areapplicable to a vast number of MRI applications, including but notlimited to any such application involving two-point Dixon imagingtechniques with flexible echo times.

Embodiments of the disclosure may present an alternative postprocessingstrategy that uses a generalized signal model and features a particulartype of sequenced region growing scheme (which can be fully automated)without a need for image thresholding. As demonstrated below, using suchembodiments, one can realize more successful water and fat separation.For example, water and fat separation has been achieved with phantom andin vivo images by a 3D dual-echo acquisition with flexible echo times.The sequenced region growing scheme of the present disclosure, which canhandle input images with more flexible phases, can lead to a wide rangeof applications in phase-sensitive MRI, as will be recognized by thosehaving ordinary skill in the art. As but one example: because of theincrease in flexibility associated with input images having flexibleecho time, a less efficient dual echo image acquisition with unipolarflyback readout gradients may be used as a practical alternative to amore efficient bipolar acquisition given its advantage of having nooff-resonance related spatial misregistration between the two inputimages along a frequency-encode direction. As an another example, atriple-echo readout that maximizes the data acquisition efficiency in afast spin echo pulse sequence, or in a spin echo pulse sequence, or in abalanced steady state free precession sequence, may be used to acquirethree images in a single acquisition. In this case, the two images fromthe 1^(st) echo and the 2^(nd) echo may be processed to generate one setof water-only and fat-only images, and the two images from the 2^(nd)echo and the 3^(rd) echo may be processed to generate a second set ofwater-only and fat-only images. The two sets of water-only and fat-onlyimages may be combined to yield a final set of water-only and fat-onlyimages with improved signal-to-noise ratio.

In one respect, embodiments of the present disclosure involve methodsfor phase-sensitive MRI to separate an intrinsic signal phase from acoexistent background or error phase, which could be due to fieldinhomogeneity or other system imperfections. For many applications, suchas Dixon chemical shift imaging and phase sensitive inversion recoveryimaging, the background or error phase usually varies slowly in spacefrom pixel to pixel. The intrinsic phase, on other hand, may bedetermined by tissue distribution and can have sudden spatial changes.The sequenced region growing methods disclosed here are able to handlebackground or error phase correction in the presence of regions of lowsignal-to-noise ratio and/or of large image artifacts, and is in generalapplicable to applications such as Dixon water and fat imaging withflexible echo times or single-point Dixon silicone specific imaging.

In another respect, methods are provided that include steps foracquiring a plurality of MRI data signals and forming complex imagesfrom the data signals. In some embodiments, the data may be acquiredfrom multiple slices, multiple receiver coils, or even at different timepoints as dynamic series. Further, a pulse sequence and a partiallyparallel imaging technique, such as a sensitivity encoding (SENSE)technique, may be performed to acquire the data. The data may be anopposed-phase echo and an in-phase echo of a first and second signaldata, or it may have flexible phases that do not have in- andopposed-phases. In some embodiments, the echo may be acquired byperforming a gradient-echo dual-echo sequence (e.g., a two-dimensionalgradient-echo dual-echo sequence or a three-dimensional gradient-echodual-echo sequence). In other embodiments, the echo may be acquired byperforming a two-dimensional spin echo pulse sequence. Alternatively,the echo may be acquired by performing a fast spin echo sequence (e.g.,a two-dimensional sequence or three-dimensional fast spin echosequence), a spin echo sequence, or a balanced steady state freeprecession sequence (e.g., a two-dimensional or a three-dimensionalsequence). In the fast spin echo, spin echo, or balanced steady statefree precession sequences, it may be preferable to use a triple echoreadout for maximal data acquisition efficiency. In some respects, datamay be acquired from an inversion recovery pulse sequence. The data maybe acquired from an inversion recovery fast spin echo sequence (e.g.,two-dimensional sequence or three-dimensional fast spin echo sequence).Alternatively, the data may be acquired from an inversion recoverytwo-dimensional or three-dimensional gradient echo sequence.

In other respects, data may be acquired from a one-point Dixon echo,which includes water and fat signals or further includes siliconesignals. In one embodiment, the one-point Dixon data may be acquiredfrom a gradient-echo sequence with a flexible echo time (e.g.,two-dimensional or three-dimensional gradient-echo sequence). In otherembodiments, one-point Dixon data may be acquired by time-shiftingconventional spin echo, such as in a two-dimensional spin echo sequence.Alternatively, the one point Dixon data may be acquired from atwo-dimensional or three-dimensional fast spin echo sequence. Further,the one point Dixon data may be acquired with an echo shift in any ofthe pulse sequences so that water and fat signals are substantiallyin-phase and the silicone signal is substantially out-of-phase with thewater and fat signals. Subsequent processing using the disclosed methodsallow for the generation of silicone-only images and silicone-suppressedimages.

Certain embodiments of the present disclosure involve a particular typeof sequenced region growing process that may be followed with algebraiccalculations, which can yield a fat-only image and a water-only image inthe case of Dixon chemical shift imaging. Alternatively, phase sensitiveinversion recovery image can be taken as the real part of a phasecorrected inversion recovery image. These images may then be displayedor archived using output and storage devices. Other uses for flexiblephase processing include imaging of silicone, such as in breast imagingof silicone breast implants.

In other respects, systems or apparatuses are disclosed. Embodiments ofa system may include a magnetic resonance imaging (MRI) scanner capableof running a pulse sequence such as a fast gradient-echo dual-echosequence, a controller, and an output device. The MRI scanner may beadapted to provide a plurality of data signals following a scan. Using apulse sequence such as the fast gradient-echo dual-echo pulse sequence,a plurality of data signals may be produced, collected, and sent to thecontroller for processing. The controller may receive the data signalsand implement image reconstruction and a phase correction algorithm toproduce an image or images (e.g., a water-only image, a fat-only image,etc). The system may additionally include a processor and a memorycomprising machine executable code configured to perform imageprocessing steps.

In one respect, embodiments of this disclosure may involve acomputerized method for generating a phase corrected magnetic resonanceimage or images. A magnetic resonance image or images containingbackground or error phase information is acquired. Two vector images Aand B are calculated either explicitly or implicitly using the acquiredimage or images so that a vector orientation by one of the two vectorimages at a pixel is substantially determined by the background or errorphase at the pixel, and the vector orientation at the pixel by the othervector image is substantially different from that determined by thebackground or error phase at the pixel. A sequenced region growing phasecorrection algorithm is applied to the vector images A and B toconstruct a new vector image V, wherein the algorithm includes:

-   -   (i) selecting an initial seed pixel or pixels and assigning        either A or B of the initial seed pixel or pixels as a value of        V for the initial seed pixel or pixels;    -   (ii) selecting a secondary seed pixel and selecting either A or        B of the secondary seed pixel as a value of V for the secondary        seed pixel based on whether A or B of the secondary seed pixel        has a smaller angular difference with an estimated V for the        secondary seed pixel;    -   (iii) determining for the secondary seed pixel a local quality        metric for each of the nearest neighbor pixels of the secondary        seed pixel for which V has not been determined and assigning a        priority to each of the nearest neighbor pixels using the local        quality metric in order to determine the sequence by which each        of the nearest neighbor pixels is to be selected as a further        seed pixel; and    -   (iv) repeating the steps of (ii) and (iii) to complete the        sequenced region growing with respect to further seed pixels and        to construct the vector image V so that a vector orientation of        V at each pixel is substantially determined by the background or        error phase at the pixel.        The phase corrected magnetic resonance image or images may be        generated from the acquired magnetic resonance image or images        using the vector image V, and the phase corrected magnetic        resonance image or images may be displayed or archived.

In other respects, embodiments may involve correcting vector images Aand B with a global linear error phase correction along one or moredimensions prior to performing the sequenced region growing. A low-passfilter may be applied to vector image V before generating the phasecorrected magnetic resonance image or images. Amplitudes of the vectorimages A and B at a pixel may be weighted by a signal amplitude at thepixel. An initial seed pixel or pixels may be selected from ahigh-quality region, where high-quality includes a predeterminedsignal-to-noise ratio or a predetermined local orientational coherencefor the vector images A or B. An initial seed pixel or pixels and thevalue of V at the initial seed pixel or pixels may be selected based onan orientational coherence of either A or B at the initial seed pixel orpixels with V at a spatially or temporally neighboring pixel or pixelsof a spatially or temporally neighboring image for which V is alreadyknown or has been determined. An initial seed pixel or pixels may beplaced onto a high priority pixel stack or stacks among a series ofpixel stacks that are initially empty and which facilitate a sequencingof the sequenced region growing. A pixel may be selected as a secondaryseed pixel if it has not been processed previously as a seed pixel andit is on a pixel stack that has a highest priority among pixel stacksthat contain at least one pixel that has not been processed as a seedpixel.

In other respects, embodiments may involve a local quality metric of apixel being calculated as the smaller of two orientational differencesbetween A and B of the pixel with an estimated V for the pixel. Theestimated V for the pixel may be a zeroth order estimation calculated asan average of V for pixels located within a neighboring region of thepixel and for which V has been previously determined. The estimated Vfor the pixel may be a first order estimation that includes an averageand a linear expansion of V for pixels that are located within aneighboring region of the pixel and for which V has been previouslydetermined. A size of the neighboring region may be either fixed oradaptively adjusted based on a local quality metric for the pixel. Themaximum possible range of 0-π for the angular difference between any twovectors may be used to gauge and bin the local quality metric and toplace a pixel onto a pixel stack. The pixel stack covering a subrange of0-π for the quality metric may be assigned a priority, where a pixelstack of a higher priority is for receiving pixels with a smallerquality metric, and a pixel stack of a lower priority is for receivingpixels with a larger quality metric. The priority of a pixel stack fromwhich a pixel is selected as a secondary seed pixel may be recorded forthe sequenced region growing as a quality metric index to reflect anintegrity of the sequenced region growing. The quality metric index maybe used to automatically segment an image into different segments ofpossible inconsistent region growing and then to combine the differentsegments into an overall consistent region growing to form a finalvector image V.

In other respects, embodiments may involve a value of the vector A foran initial seed pixel being assigned as V_(A), and a sequenced regiongrowing being performed to construct a vector image V_(A), where a valueof the vector B for the same initial seed pixel is assigned as V_(B),and another sequenced region growing is performed to construct a vectorimage V_(B). Either vector image V_(A) or vector image V_(B) may be setto a final vector image V, depending on whether vector image V_(A) orvector image V_(B) has a greater overall orientational smoothness.

In other respects, embodiments may involve the sequenced region growingbeing performed in two spatial dimensions. The sequenced region growingmay be performed in three spatial dimensions. The sequenced regiongrowing may be performed by including the temporal dimension for aseries of dynamically acquired images.

In other respects, embodiments may involve acquiring two-point Dixonwater and fat images, wherein a first image S1 is acquired at a firstecho time TE1 and a second image S2 is acquired at a second echo timeTE2. Acquiring two-point Dixon water and fat images may involve usingdual-echo bipolar readout gradients. Acquiring two-point Dixon water andfat images may involve using dual-echo unipolar readout gradients.Acquiring two-point Dixon water and fat images may involve usingtriple-echo readout gradients. Acquiring two-point Dixon water and fatimages may involve using interleaved single echo readout gradients.

In other respects, embodiments may involve selection of TE1 and TE2being flexible except to avoid a small orientational difference betweenvector image A and vector image B. The images S₁ and S₂ may be expressedaccording to the following equations:

S ₁=(W+δ ₁ Fe ^(iθ) ¹ )P ₁

S ₂=(W+δ ₂ Fe ^(iθ) ² )P ₁ P

where W and F are amplitudes for water and fat respectively, P₁ is aphase factor of image S₁, P is an additional phase factor of image S₂relative to image S₁ and is determined by a background or error phase,and one may determine by an image based pre-calibration an amplitudeattenuation factor (δ₁, δ₂) and phase (θ₁, θ₂) as a function of two echotimes (TE1, TE2) for the fat signal. Pre-calibration of (δ₁, δ₂) may beperformed in part by determining an echo time dependence of a signalamplitude of a known fat-only image region, and pre-calibration of (θ₁,θ₂) may be performed in part by determining an echo time dependence of aphase discontinuity between a known fat-only image region and aneighboring known water-only region. The pre-calibration may beperformed for a given pulse sequence, a scan protocol, or a magneticfield strength.

In other respects, embodiments may involve the images S₁ and S₂ beingused to generate two vector images A and B as expressed according to thefollowing equations:

A=S* ₁ S ₂ [Q _(A)+δ₁(1−Q _(A))e ^(iθ) ¹ ][Q _(A)+δ₂(1−Q _(A))e ^(−iθ) ²]

B=S* ₁ S ₂ [Q _(B)+δ₁(1−Q _(B))e ^(iθ) ¹ ][Q _(B)+δ₂(1−Q _(B))e ^(−iθ) ²]

where Q_(A) and Q_(B) are the two mathematically possible solutions ofthe following quadratic equation of Q, which is defined as

$Q = \frac{W}{W + F}$

(i.e., me water traction tor a given pixel):

[(1+δ₂ ²−2δ₂ cos θ₂)M ₁−(1+δ₁ ²−2δ₁ cos θ₁)M ₂ ]Q ²−2[(δ₂ ²−δ₂ cos θ₂)M₁−(δ₁ ²−δ₁ cos θ₁)M ₂ ]Q+[(M ₁δ₂ ² −M ₂δ₁ ²)]=0

where M₁ and M₂ are the square of the amplitudes of the images S₁ andS₂, respectively (i.e., M₁=|S₁|² and M₂=|S₂|²). The vector images may befurther normalized and weighted by a signal amplitude, such as:

$A^{\prime} = {\frac{A}{A}\sqrt{M_{1} + M_{2}}}$$B^{\prime} = {\frac{B}{B}\sqrt{M_{1} + M_{2}}}$

where again, M₁=|S₁|² and M₂=|S₂|². Sequenced region growing may be usedto construct a vector image V from the two vector images A and B. Thevector image V may be used to phase correct and remove the phase factorP from the image S₂, the phase corrected S₂ may be combined with S₁ tosolve for WP₁ and FP₁, and then to generate a water-only image and afat-only image according to the following equations:

W=Real{(WP ₁) WP ₁ */| WP ₁ |}

F=Real{(FP ₁) FP ₁ */| FP ₁ |}

where Real{ . . . } is to take the real component of its complexargument, * is to take the complex conjugate of its argument, and WP₁and FP₁ represent low-pass filtering of WP₁ and FP₁, respectively.

In other respects, embodiments may involve acquiring a single-pointDixon water and fat image wherein a flexible echo time TE is used andthe acquired magnetic resonance image is expressed as: S=(W+Fe^(iθ))P,where θ is dependent on TE and the dependence is determined with animage-based pre-calibration, and P(≡e^(iφ)) is a phase factor for theimage S. The vector image A may be set to S and the vector image B maybe set to Se^(−iθ). A sequenced region growing may be used to constructa vector image V from the two vector images A and B, the vector image Vmay be used to phase correct or remove P from S to form S′, and awater-only image and a fat-only image may be generated according to:

F=Imag{S′}/sin θ

W=Real{S′−F cos θ}

where Real{ . . . } and Imag{ . . . } are to take the real and imaginarycomponents of their component, respectively.

In other respects, embodiments may involve acquiring a single-pointsilicone specific image where an echo time TE when water and fat signalsare substantially in-phase is used, and the acquired magnetic resonanceimage may be expressed according to the following equation:

S=(W+F+Ie ^(iθ))P

where θ is determined with an image-based pre-calibration for the echotime TE as a phase discontinuity of a known silicone-only image regionand a neighboring known water or fat only image region, and P(≡e^(iφ))is a phase factor for the image S. Vector image A may be set to S andvector image B may be set to Se^(−iθ). A sequenced region growing may beused to construct a vector image V from the two vector images A and B,the vector image V may be used to phase correct or remove P from S toform S′, and a silicone-only image and a silicone-suppressed image maybe generated according to:

I=Imag{S′}/sin θ

W+F=Real{S′−I cos θ}

where Real{ . . . } and Imag{ . . . } are to take the real and imaginarycomponents of their component, respectively.

In other respects, embodiments may involve acquiring an inversionrecovery image at an inversion recovery time TI and the image may beexpressed according to the following equation:

S=Ie ^(iθ)

where I is a signal magnitude and θ is a measured signal phase thatcomprises a background or error phase and an intrinsic signal phase.Vector image A may be set to S and vector image B may be set to −S. Asequenced region growing may be used to construct a vector image V fromthe two vector images A and B, the vector image V may be used to phasecorrect the image S, and the phase corrected image S may be displayedand archived as a phase sensitive inversion recovery image.

In other respects, embodiments may involve any apparatuses or systemsconfigured to perform one or more steps disclosed herein in anycombination, using for example one or more processors and memory devicescoupled to imaging equipment. In still other respects, embodiments mayinvolve software configured to perform one or more steps disclosedherein in any combination.

Other features and associated advantages will become apparent withreference to the following detailed description of specific, exampleembodiments in connection with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The following drawings form part of the present specification and areincluded to further demonstrate certain aspects of disclosedembodiments. The drawings do not limit the invention but simply offerexamples.

FIG. 1 is an illustration of an MRI apparatus and system in accordancewith embodiments of this disclosure.

FIGS. 2A and 2B are flow charts illustrating phase correction steps inaccordance with embodiments of this disclosure.

FIG. 3 is another flow chart illustrating phase correction steps inaccordance with embodiments of this disclosure.

FIGS. 4-7 are water- and fat-only images generated and displayed inaccordance with examples of this disclosure.

DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

The present invention includes methods, systems, apparatuses, andnon-transitory computer readable media that can make use of efficientand robust phase correction algorithms, which can be applied toapplications such as, but not limited to, all types of phase sensitiveMRI. One application used for illustration here is a 2PD (2-point Dixon)technique with a commercially available fast gradient-echo dual-echodata acquisition pulse sequence and a phase-correction algorithm toproduce higher resolution images taken from an MRI scan. In otherembodiments, a phase correction algorithm according to embodiments ofthis disclosure may be used in applications such as, but not limited to,one-point Dixon (1PD) techniques for water and fat imaging, one-pointDixon (1PD) techniques for silicone-specific imaging, and phasesensitive inversion recovery imaging. For Dixon chemical shift imaging,a phase correction algorithm according to embodiments of this disclosuremay be applied to data collected with different types of pulsesequences, such as conventional spin echo pulse sequences and fast spinecho pulse sequences. The data collected may be from a two-dimensionalacquisition or from a three-dimensional acquisition. The data collectedmay also be from time-series studies such as when used to study contrastagent uptake behavior after a contrast agent is injected into a patient.Alternatively, the data may be acquired with partially parallel imagingtechniques such as the sensitivity encoding (SENSE) technique. In theseembodiments, after the reconstruction of the acquired images, techniquesare provided for correcting background or error phase that may arise asa result of field inhomogeneity or other system imperfections.

In one respect, phase-correction algorithms according to embodiments ofthis disclosure involve a particular type of sequenced region growingprocess. The sequence of the region growing may be determined using aquality metric of seed pixels, and selection of the seed pixels may beautomatically sorted-out using a series of pixel stacks that bin andhold the seed pixels. The direction for the phase vector of each of thepixels may be determined from an estimated direction using both theamplitude and the phase of the phase vectors of those pixels alreadydetermined and that are located within a neighboring area, such as anarea defined by a boxcar in two-dimensions or by a regular cuboid inthree-dimensions, typically centered around a pixel under consideration.Other shapes and various sizes—fixed and adaptively adjusted—can reflecta suitable neighboring area.

In FIG. 1, an MRI apparatus, in accordance with an embodiment of thepresent disclosure, is presented. The MRI apparatus includes a scanner100, a controller 102, a processor 104, a memory 106, output devicessuch as a display screen 108, an output printing device 110, and inputdevices such as a keyboard 112 and a mouse 114. A server 116 may also beincluded that may communicate with controller 102 and input and outputdevices such as keyboard 112 and mouse 114. The server 116 and thecontroller 102 may comprise one or more processors such as processor 104coupled to, and in communication with, one or more memories such asmemory 106. The server 116 may be coupled to the controller 102, andsuch coupling may be through intermediate devices or a networkconnection, such as the Internet, or otherwise.

In certain embodiments of this disclosure, error phase correction may beimplemented through the use of, for example, processor 104 and memory106 in the controller 102 or associated with the server 116.

Techniques of the present disclosure may be applied to certain, existingMRI hardware commercially available or known in the art throughappropriate programming or data processing techniques, as will beunderstood to those having ordinary skill in the art, and further asdescribed herein.

In one embodiment, a patient 101 may be placed inside scanner 100. Thecontroller 102 may control aspects of imaging and obtain data, processthe data to obtain desired image(s), and output final image(s) to anoutput device of choice, such as a display screen 108, printing device110, an electronic storage (local or distant via, for example, a networkconnection). Images may also be transmitted through a network connectionto server 116. Other transmission techniques known in the art may alsobe utilized.

Two-Point Dixon Water and Fat Imaging

Representing one group of embodiments, the following discloses a signalmodel and mathematics suitable for two-point Dixon water and fat imagingtechniques using flexible echo times, among other applications as willbe apparent to those having ordinary skill in the art.

Two raw images acquired at echo times TE1 and TE2 may be expressed as:

S ₁=(W+δ ₁ Fe ^(iθ) ¹ )P ₁  [1]

S ₂=(W+δ ₂ Fe ^(iθ) ² )P ₁ P  [2]

in which W and F represent the amplitudes of water and fat,respectively. (δ₁, δ₂) and (θ₁, θ₂) are the amplitude attenuationfactors and chemical shift-related phases of fat at TE1 and TE2,respectively. P₁ is the phasor (defined as a complex number with a unitamplitude) of the image S₁ and includes the effects of all of its phasefactors (e.g., magnetic field inhomogeneity) except that of the chemicalshift of fat. P is an additional phasor of S₂ relative to S₁. For givenTE1/TE2, (δ₁, δ₂) and (θ₁, θ₂) can be considered known parameters via animage-based precalibration without assuming any specific spectral modelor resorting to measurements by magnetic resonance spectroscopy(described below).

The following can be calculated using Eqs. [1-2]:

M ₁=(W ²+δ₁ ² F ²+2δ₁ WF cos θ₁)  [3]

M ₂=(W ²+δ₂ ² F ²+2δ₂ WF cos θ₂)  [4]

in which M₁=|S₁|² and M₂=|S₂|².

Analogous to Berglund et. al., (Magnetic Resonance in Medicine65:994-1004 (2011)), one may define:

$\begin{matrix}{Q = \frac{W}{W + F}} & \lbrack 5\rbrack\end{matrix}$

which represents the water fraction for a given image pixel.

Eqs. [3 and 4] can be rewritten as:

$\begin{matrix}{\frac{M_{1}M_{2}}{\left( {W + F} \right)^{2}} = {\left\lbrack {\left( \frac{W}{W + F} \right)^{2} + {\delta_{1}^{2}\left( \frac{F}{W + F} \right)}^{2} + {2\; \delta_{1}\cos \mspace{11mu} \theta_{1}\frac{WF}{\left( {W + F} \right)^{2}}}} \right\rbrack M_{2}}} & \lbrack 6\rbrack \\{\frac{M_{1}M_{2}}{\left( {W + F} \right)^{2}} = {\left\lbrack {\left( \frac{W}{W + F} \right)^{2} + {\delta_{2}^{2}\left( \frac{F}{W + F} \right)}^{2} + {2\; \delta_{2}\cos \mspace{11mu} \theta_{2}\frac{WF}{\left( {W + F} \right)^{2}}}} \right\rbrack M_{1}}} & \lbrack 7\rbrack\end{matrix}$

Combining Eqs. [6 and 7] and recognizing that

${1 - Q} = \frac{F}{W + F}$

one gets:

[(1+δ₂ ²−2δ₂ cos θ₂)M ₁−(1+δ₁ ²−2δ₁ cos θ₁)M ₂ ]Q ²−2[(δ₂ ²−δ₂ cos θ₂)M₁−(δ₁ ²−δ₁ cos θ₁)M ₂ ]Q+[(M ₁δ₂ ² −M ₂δ₁ ²)]=0  [8]

This is a quadratic equation for Q. One may define:

a′ ₁=[(1+δ₂ ²−2δ₂ cos θ₂)M ₁−(1+δ₁ ²−2δ₁ cos θ₁)M ₂]  [9]

a′ ₂=−2[(δ₂ ²−δ₂ cos θ₂)M ₁−(δ₁ ²−δ₁ cos θ₁)M ₂]  [10]

a′ ₃=[(M ₁δ₂ ² −M ₂δ₁ ²)]  [11]

Eq. [8] can be rewritten as:

a′ ₁ Q ² +a′ ₂ Q+a′ ₃=0  [12]

which has the following two mathematically possible solutions:

$\begin{matrix}{Q_{A,B} = {\frac{{- a_{2}^{\prime}} \pm \sqrt{a_{2}^{\prime 2} - {4a_{1}^{\prime}a_{3}^{\prime}}}}{2a_{1}^{\prime}} = \frac{a_{2} \pm \sqrt{a_{3}}}{a_{1}}}} & \lbrack 13\rbrack\end{matrix}$

in which:

$\begin{matrix}{a_{1} = {a_{1}^{\prime}\left\lbrack {{\left( {1 + \delta_{2}^{2} - {2\; \delta_{2}\cos \mspace{11mu} \theta_{2}}} \right)M_{1}} - {\left( {1 + \delta_{1}^{2} - {2\; \delta_{1}\cos \mspace{11mu} \theta_{1}}} \right)M_{2}}} \right\rbrack}} & \lbrack 14\rbrack \\{a_{2} = {{- \frac{a_{2}^{\prime}}{2}} = \left\lbrack {{\left( {\delta_{2}^{2} - {\delta_{2}\cos \mspace{11mu} \theta_{2}}} \right)M_{1}} - {\left( {\delta_{1}^{2} - {\delta_{1}\cos \mspace{11mu} \theta_{1}}} \right)M_{2}}} \right\rbrack}} & \lbrack 15\rbrack \\\begin{matrix}{a_{3} = \frac{a_{2}^{\prime 2} - {4a_{1}^{\prime}a_{3}^{\prime}}}{4}} \\{= \left\lbrack {{\left( {\delta_{1}^{2} + \delta_{2}^{2} - {2\delta_{1}\delta_{2}\cos \mspace{11mu} \theta_{1}\cos \mspace{11mu} \theta_{2}}} \right)M_{1}M_{2}} - {\delta_{2}^{2}\sin^{2}\theta_{2}M_{1}^{2}} -} \right.} \\\left. {\delta_{1}^{2}\sin^{2}\theta_{1}M_{2}^{2}} \right\rbrack\end{matrix} & \lbrack 16\rbrack\end{matrix}$

In general, only one of the two solutions in Eq. [13] corresponds to thetrue and physical solution for the water fraction Q.

Determining the true and physical solution for the water fraction Q forall the pixels of an image is in general a very challenging problem.Here, a particular type of novel sequenced region growing based phasecorrection may be used to obtain solutions. At this point, selecting thetrue and physical solution for Q from the two sets of choices in Eq.[13] requires consideration of the phase of the acquired signals (whichis removed in Eqs. [3] and [4] by the absolute value operation).

For this purpose, Eqs. [1-2] can be combined to yield the following:

S* ₁ S ₂=(W+δ ₁ Fe ^(−iθ) ¹ )(W+δ ₂ Fe ^(iθ) ² )P  [17]

Dividing Eq. [17] by (W+F)², one gets:

$\begin{matrix}{\frac{S_{1}^{*}S_{2}}{\left( {W + F} \right)^{2}} = {{\left\lbrack {Q + {{\delta_{1}\left( {1 - Q} \right)}^{{- }\; \theta_{1}}}} \right\rbrack \left\lbrack {Q + {{\delta_{2}\left( {1 - Q} \right)}^{\; \theta_{2}}}} \right\rbrack}P}} & \lbrack 18\rbrack\end{matrix}$

Using the two solutions from Eq. [13], the following two vectors can beformed:

A=S* ₁ S ₂ [Q _(A)+δ₁(1−Q _(A))e ^(iθ) ¹ ][Q _(A)+δ₂(1−Q _(A))e ^(iθ) ²]  [19]

B=S* ₁ S ₂ [Q _(B)+δ₁(1−Q _(B))e ^(iθ) ¹ ][Q _(B)+δ₂(1−Q _(B))e ^(iθ) ²]  [20]

The amplitudes of A and B are to the 2^(nd) power order of W and F. Forthe following processing, they can be weighted differently, e.g., to beapproximately linearly proportional to W and F to form a new set of Aand B:

$\begin{matrix}{A^{\prime} = {\frac{A}{A}\sqrt{M_{1} + M_{2}}}} & \lbrack 21\rbrack \\{B^{\prime} = {\frac{B}{B}\sqrt{M_{1} + M_{2}}}} & \lbrack 22\rbrack\end{matrix}$

Other forms of weighting can also be used if desired, as will berecognized by those having ordinary skill in the art. Here, note thatthe direction represented by either A′ or B′ will be substantially equalto that represented by P depending on whether the correct, true physicalsolution for Q is represented by Q_(A) or Q_(B) in Eqs. [19-20].

Because P is determined by underlying factors (e.g., magnetic fieldinhomogeneity) that are generally assumed to be spatially smooth, thecorrect distribution of P can be determined by constructing a vectorfield V (initially set to zero for all of the pixels) that is spatiallysmooth in its angular orientation and represented by either A′ or B′ ona pixel basis.

Again, in general, constructing such a vector field may be a verychallenging problem, especially considering the large variations of thetypes and qualities of the images encountered in medical imaging. Foroptimized processing reliability, one may generally use a particulartype of sequenced region-growing scheme according to the presentdisclosure; such a sequenced region-growing process may include thefollowing steps.

First, selecting an initial seed pixel or pixels and assigning either Aor B of the initial seed pixel or pixels as a value of V for the initialseed pixel or pixels.

Second, selecting a secondary seed pixel and selecting either A or B ofthe secondary seed pixel as a value of V for the secondary seed pixelbased on whether A or B of the secondary seed pixel has a smallerangular difference with an estimated V for the secondary seed pixel. Inone embodiment, the estimated V for a secondary seed pixel is a zerothorder estimation calculated as an average or sum of V for pixels locatedwithin a neighboring region of the secondary seed pixel and for which Vhas been previously determined. In this case, the two angulardifferences may be conveniently calculated as follows:

α_(AV)=|angle(A′*(ΣV)*)|  [23]

α_(BV)=|angle(B′*(ΣV)*)|  [24]

where summation is performed over a group of pixels that lie within aboxcar or cuboid neighborhood of the secondary seed pixel and whosevalues of V have been previously decided in the sequenced region growingprocess. The size of the boxcar can be either fixed or adaptivelyadjusted (see the step below). The value of V for the secondary seedpixel will be set either to its A′ or B′ depending on which of the twophase differences by Eqs. [23-24] is smaller. For example, ifα_(AV)<α_(BV), the value of V for the secondary seed pixel will be setits A′.

Third, a local quality metric may be determined by calculating twoangular differences between A′ and B′ for each of the seed's nearestneighbor pixels (whose value of V is still zero because it has not yetbeen processed as a seed pixel) with an estimated V of the same nearestneighbor pixel. In one embodiment, the estimated V for a nearestneighbor pixel is a zeroth order estimation calculated as an average orsum of V for pixels located within a neighboring region of the nearestneighbor pixel and for which V has been previously determined. In thiscase, the two angular differences may be conveniently calculated asfollows:

β_(AV)=|angle(A′*(ΣV)*)|  [25]

β_(BV)=|angle(B′*(ΣV)*)|  [26]

where summation is again performed over a group of pixels that liewithin a boxcar or cuboid neighborhood of the nearest neighbor pixel andwhose values of V have been previously decided in the region growingprocess. The boxcar size can be either the same or different from thatused in Eqs. [23-24].

One difference between the calculations in Eqs. [23-24] and in Eqs.[25-26] is that the calculation in Eqs. [25-26] will include the V ofthe seed pixel, which is now decided after the second step. The smallerof the two phase differences by Eqs. [25-26] may then used as a qualitymetric to decide where the nearest neighbor pixel is placed onto a stack(or bin, or other comparable storage or sorting technique) by comparingthe smaller of the two phase differences with a maximum possible rangeof 0 to π. Among a series of prioritized and initially-empty pixelstacks, the nearest neighbor pixel may be stored in a high or lowpriority pixel stack if the smaller of the two phase differences issmall or large (when compared to the range of 0 to π), respectively.

Once all the nearest neighbor pixels of the secondary seed pixel havebeen considered, a pixel from the pixel stack with the highest priorityand at least one unprocessed pixel may be selected as the next “best”new secondary seed pixel, and the same sequenced region growingprocessing may be repeated until all of the pixels have been processedas a seed pixel and the vector V of all the pixels has beensubstantially determined. Several notes can be made about the sequencedregion growing embodiments of the present disclosure.

First, before the initiation of the sequenced region growing, A′ and B′may be first corrected with a global linear error phase correction alongone or more dimensions such as described in Ma et al, Magnetic Resonancein Medicine, 2008, 60(5):1250, which is incorporated herein byreference. This pre-treatment step may be especially useful when globallinear phase errors exist due to echo center shift for two echoes.

Second, two separate sequenced region growing processes may be performedby selecting A′ or B′ as the value of V for a very initial seed pixel.Two vector maps V_(A) and V_(B) may be generated. The correct one isexpected to have an overall smoother spatial phase variation. And thiscondition can be detected by calculating and comparing the following twoquantities:

T _(A) =Σ|ΣV _(A)|  [27]

T _(B) =Σ|ΣV _(B)|  [28]

in which an image is first divided into sub-images (e.g., a 256×256image may be divided into images of the size 16×16), and the innersummations in Eqs [27-28] may be performed over all the pixels withineach and every subimage. The outer summations in Eqs. [27-28] may beperformed over all the sub-images. If T_(A)>T_(B), then V_(A) isdetermined to be the correct V. On the other hand, if T_(A)<T_(B), thenV_(B) is determined to be the correct V.

Third, a “quality” of the sequenced region growing process can bemonitored and recorded using a quality index which records the pixelstack number or the quality metric of each seed pixel when it isselected as a seed as a function of the sequenced growing sequence.During the sequenced region growing process, the “quality” index can beused to apply enhanced processing selectively only to pixels that areprone to errors in the processing. For example, pixels that are in lowpriority pixel stacks have small phase variation and may not need theenhanced processing. Conversely, pixels that are in very high prioritypixel stacks have very large phase variations and therefore are likelyto correspond to background noise and also may not need enhancedprocessing. Pixels that are in intermediate priority pixel stacks may beprone to errors, and enhanced processing may therefore be helpful.

One type of enhanced processing that can optionally be applied for thosepixels that have an intermediate “quality” index is to maximize theamplitude of the local vector summation of the alternative solutions(i.e., A or B) for the vector V:

Z=|ΣV|  [29]

in which the summation is performed over the pixels that have beenprocessed by the sequenced region growing and lie within a small boxcaror cuboid region. Z is maximized by testing A or B as the correctsolution of V for those pixels. For example, if Z is bigger when A isused for a pixel than when B is used, then A will be selected as thecorrect solution of V. Alternatively, the quality index can be used todetect potentially unreliable steps of the sequenced region growing. Forexample, when the sequenced region growing is crossing noisy regionsbetween two disconnected tissues in an image (e.g., an image of two legsacquired in an axial plane), the quality index is expected to recordlarge variations due to the random fluctuation of noise. Phasecorrection among the different disconnected tissues can be madeconsistent by using the quality index to automatically segment an imageinto segments of consistent region growing. Different segments can thenbe made consistent by testing alternative solutions from the differentsegments on a region-level.

Fourth, as indicated previously, the entire region growing process canbe generalized to be 3-dimensional in space or even to the timedimension.

After the vector image V is determined by the sequenced region growingembodiments of this disclosure, it can be low-pass filtered. The phasorP can then be taken as a normalized V and removed from Eq. [2]. Thecorrected Eq. [2] can then be combined with Eq. [1] to solve for WP₁ andFP₁. Because P₁ is also expected to be spatially smooth in its angularorientation, WP₁ and FP₁ can be low-pass filtered to obtain WP₁ and FP₁and then the SNR-optimized W and F:

W=Real{(WP ₁) WP ₁ */| WP ₁ |}  [30]

F=Real{(FP ₁) FP ₁ */| FP ₁ |}  [31]

Image-Based Pre-Calibration of the Fat Signal Model

Pre-calibration of the dependence of (δ₁, δ₂) and (θ₁, θ₂) on TE₁ andTE₂: The dependence of (δ₁, δ₂) and (θ₁, θ₂) on TE₁ and TE₂ can beaffected by many factors such as the spectral complexity of fat andpulse sequence related scan parameters such as repetition time (TR) andflip angle as well as the magnetic field strength that is used forimaging. Further, different spectral components of fat not only havedifferent resonance frequencies and relative amplitudes, but may alsohave different relaxation time constants. Because of this complexity, animage-based pre-calibration procedure may be used to account for allthese factors in one embodiment.

In this embodiment, one can determine (θ₁, θ₂) as a function of TE bymeasuring the phase discontinuity between a known water-dominant region(e.g., muscle) and a known neighboring fat-dominant region (e.g.,subcutaneous fat). One can determine (δ₁, δ₂) as a function of TE bymeasuring the image intensity variation of a fixed known fat-dominantregion (e.g., subcutaneous fat). Because fat in different subjects oranatomical locations is known to have very similar compositions, onlyone in vivo calibration may be required to account for the effects ofcomplex fat spectra. Different calibrations can be performed to accountfor other contributing factors (e.g., vastly different scan protocols orfield strengths). These image-based pre-calibration results can then bestored in a look-up table or fitted to one or more functions to be usedin the phase correction algorithm.

Single Point Dixon Water and Fat Imaging and Single Point Dixon SiliconeImaging

In a single point Dixon water and fat imaging application, an image isacquired at a flexible echo time TE, and the image may be expressed as

S=(W+Fe ^(iθ))P

where θ is dependent on TE and the dependence may determined with animage-based pre-calibration, and P(≡e^(iφ)) is the phase factor for theimage S. In this case, the vector image A may be equal to S and thevector image B may be equal to Se^(−iθ). The same sequenced regiongrowing scheme as described above may then be performed on A and B toconstruct a vector image V. The vector image V is used to phase corrector remove P from S to form S′, and a water-only image and a fat-onlyimage are generated according to:

F=Imag{S′}/sin θ

W=Real{S′−F cos θ}

where Real{ . . . } and Imag{ . . . } are to take the real and imaginarycomponents of their component, respectively.

Additionally, silicone-specific imaging using a single-point Dixontechnique can be accomplished where an image is acquired at an echo timeTE when water and fat signals are substantially in-phase and the imageis represented as:

S=(W+F+Ie ^(iθ))P

where θ is determined with an image-based pre-calibration for thischosen TE, and P(≡e^(iφ)) is the phase factor for the image S. In thiscase, vector image A is equal to S and vector image B is equal toSe^(−iθ).

The sequenced region growing scheme may then be performed on A and B toconstruct a vector image V. The vector image V is used to phase corrector remove P from S to form S′, and a silicone-only image and asilicone-suppressed image are generated according to:

I=Imag{S′}/sin θ

W+F=Real{S′−I cos θ}

where Real{ . . . } and Imag{ . . . } are to take the real and imaginarycomponents of their component, respectively.

Phase Sensitive Inversion Recovery Imaging

Using an inversion recovery technique an image may be acquired at acertain inversion recovery time TI and the image may be represented as:

S=Ie ^(iθ)

where I is the signal magnitude and θ is the measured signal phase thatcomprises a background or error phase and an intrinsic signal phase. Inthis case, the vector image A is S and the vector image B is −S.

The sequenced region growing scheme may then be performed on A and B toconstruct a vector image V. The vector image V is used to phase corrector remove P from S, and the phase corrected image S is displayed orarchived as a phase sensitive inversion recovery image.

FIG. 2A is a flowchart of image processing steps 200 according toembodiments of the present disclosure. Steps 200 may be used to generatea phase corrected magnetic resonance image and may follow any one ormore of the calculations noted above. These steps—or any steps disclosedhere—may be performed on a suitable processor such as processor 104 ofFIG. 1. The processor, in turn, may be coupled to, or associated withmemory 106, controller 102, or server 116.

In step 202, a magnetic resonance image containing background or errorphase information is acquired. Such information may be provided by MRIequipment such as that shown in FIG. 1 or otherwise. In step 204, twovector images A and B are calculated using the acquired image or imagesso that a vector orientation by one of the two vector images at a pixelis substantially determined by the background or error phase at thepixel, and the vector orientation at the pixel by the other vector imageis substantially different from that determined by the background orerror phase at the pixel.

In step 206, a sequenced region growing phase correction algorithm isapplied to the vector images A and B to construct a new vector image V.A global linear phase correction, or other corrections, can be appliedprior to the region growing phase correction algorithm.

In step 208, the phase corrected magnetic resonance image or images aregenerated from the acquired magnetic resonance image or images using thevector image V. In step 212, the phase corrected magnetic resonanceimage or images are displayed or archived. Display or archiving may bedone in conjunction with the equipment of FIG. 1 or any display deviceknown in the art, including but not limited to devices that produceelectronic or hard-copy output, as well as network-connected devices.

FIG. 2B is a flowchart that is an extension of FIG. 2A and also reflectssteps 200. FIG. 2B expands step 206 of FIG. 2A according to certainembodiments of this disclosure. Steps 200 as reflected in FIG. 2B may beused to generate a phase corrected magnetic resonance image or imagesand may follow any one or more of the calculations noted above. Thesesteps—or any steps disclosed here—may be performed on a suitableprocessor such as processor 104 of FIG. 1. The processor, in turn, maybe coupled to, or associated with memory 106, controller 102, or server116.

In step 214, an initial seed pixel or pixels are selected and either Aor B of the initial seed pixel or pixels is assigned as a value of V forthe initial seed pixel or pixels. In step 216, a secondary seed pixel isselected and either A or B of the secondary seed pixel is selected as avalue of V for the secondary seed pixel based on whether A or B of thesecondary seed pixel has a smaller angular difference with an estimatedV for the secondary seed pixel. In step 218, a local quality metric isdetermined for nearest neighbor pixels of the secondary seed pixel forwhich V has not been determined; and, a priority of a nearest neighborpixel is determined using this local quality metric so that one maydetermine the sequence by which the nearest neighbor pixel is to beselected as a further seed pixel. Step 220 reflects that steps 214 and216 may be repeated to complete this sequenced region growing withrespect to further seed pixels and to construct vector image V so that avector orientation of V at each pixel is substantially determined by thebackground or error phase at the pixel.

FIG. 3 is a flowchart of image processing steps 300 according toembodiments of the present disclosure. In step 302, MRI image data isobtained (e.g., from scanning a patient 101). In step 304, two vectorimages A and B are reconstructed from the received MRI data from step302. An initial seed pixel or pixels are selected in step 306. Aninitial seed pixel may be selected randomly, or one or more seed pixelsmay be selected according to an algorithm or a predetermined sequence. Abranch may be taken after step 306.

In step 308, vector image A is selected for an initial seed pixel, andin step 310 vector image B is selected for the initial seed pixel.

Calculations in the separate branches may be done serially, in parallel,or in some combination of either. In each branch a sequenced regiongrowing process as disclosed herein may be performed as illustrated insteps 312 and 314.

A vector image V_(A) is formed in step 316 after processing all or asufficient subset of pixels, and a vector image V_(B) is formed in step318 after processing all or a sufficient subset of pixels.

The smoothness of V_(A) and V_(B) are compared in step 320, and thesmoother of the two vector images may be chosen in step 322 as thevector V, which is then used to phase correct the acquired image orimages and to generate phase corrected magnetic resonance image orimages for display or storage purposes.

Any type of MRI image or images may be subjected to image processingsteps 200 or 300, or those disclosed herein. Again, a suitable MRI imageor images may involve two point Dixon water and fat images that areacquired using flexible echo times. Image processing steps 200 and 300may be performed by—and may be integrated with, either by hardware orsoftware—any suitable MRI system, including commercially availablesystems. Similarly the processing steps of this disclosure may beimplemented on a non-transitory computer readable storage medium as anexecutable program that instructs a microprocessor to perform the steps.

The following examples are included to demonstrate aspects of specificexperiments related to this disclosure. Subject matter presented as anexample may be encompassed by the present claims or added to the claimsto define protected subject matter.

Example 1 Two-Point Dixon Example

The flexible phase postprocessing strategy, as described in detailabove, was implemented using MATLAB (MathWorks), and a 3D fast spoiledgradient-echo bipolar dual echo pulse sequence was used to collect rawdata for a water/fat phantom (consisting of water and vegetable oil) andfor the in vivo abdomen of a human subject using a 1.5T whole-body MRscanner (GE Healthcare; HDxt platform). For the in vivo imaging, aneight-channel phased array body coil was used, and the scan parameterswere as follows: TR=minimum, FOV=36×27 cm, acquisition matrix=256×192,flip angle=12°, slice thickness=4 mm, total number of slices=38, andreceiver bandwidth=±83.33 kHz. Minimum as well as different combinationsof manually selected echo times were used for the dual-echo readout. Forthe phantom imaging, an eight-channel phased array head coil and scanparameters similar to those for the in vivo scanning were used exceptthat for a fixed TE1 of 1.2 ms, TE2 varied systematically from 2.9 ms(minimum allowed) to 5.2 ms with a ΔTE of 0.1 ms; for a fixed TE2 of 4.6ms, TE1 varied systematically from 1.2 ms to 2.9 ms (maximum allowed)with a ΔTE of 0.1 ms.

Before Dixon processing, (θ₁, θ₂) can be determined as a function of TEby measuring the phase discontinuity between a known water-dominantregion (e.g., muscle) and a known neighboring fat-dominant region (e.g.,subcutaneous fat). (δ₁, δ₂) can also be determined as a function of TEby measuring the image intensity decay of a fixed fat dominant region.Because fat in different subjects or anatomical locations is known tohave very similar compositions, only one in vivo calibration is requiredto account for the effects of complex fat spectra. Differentcalibrations may be performed to account for other contributing factors(e.g., vastly different scan protocols or field strengths). The extendedphase correction algorithm was able to reconstruct separate water andfat-only images of both the phantom and abdomen in vivo for all of theselected TE1/TE2 combinations.

For example, FIGS. 4-7 show two sets of water- and fat-only images fordata acquired at TE1/TE2=1.5/3.4 ms with a corresponding precalibrated(θ₁, θ₂) of (77°, 245°) (FIG. 4, FIG. 5) and at TE1/TE2=2.2/4.4 ms witha corresponding precalibrated (θ₁, θ₂) of (140°, 305°) (FIG. 6, FIG. 7)that are closer to being out-of-phase/in-phase. The water/fat separationand overall image quality are excellent in both cases. However, thefirst set of data required shorter TR and scan times (5.5 ms and 21 s,respectively) than those for the second set of data (6.5 ms and 25 s,respectively) for otherwise identical scan parameters.

The sequenced region growing-based phase correction strategy can beimplemented as a fully automatic solution, and it is capable of robustwater and fat separation using two input images with flexible echotimes. Because of this increased flexibility, note that theless-efficient dual-echo image acquisition with unipolar flyback readoutgradients may be used as a practical alternative to the more-efficientbipolar acquisition for its advantage of having no off-resonance relatedspatial misregistration between the two input images along thefrequency-encode direction.

It will be manifest that various substitutions, modifications, additionsand/or rearrangements of the features of the invention may be madewithout deviating from the spirit and/or scope of the underlyinginventive concept. It is deemed that the spirit and/or scope of theunderlying inventive concept as defined by the appended claims and theirequivalents cover all such substitutions, modifications, additionsand/or rearrangements. For example, different schemes of selecting theinitial seed pixel or pixels and assigning the value of V for theseinitial seed pixels may be employed; Different ways of calculating thevector images A and B are possible and can be used for the two pointDixon imaging with flexible echo times or other phase sensitive magneticresonance imaging applications; The phase correction algorithm with thesequenced region growing can also be easily extended to applications inwhich more than two vectors images (e.g., A, B, C) need to be consideredto construct a final vector image V that is used for phase correction;Calculation of an estimated V for a pixel may be performed using morecomplicated method beyond a 0^(th) order or 1^(st) order estimation;Additionally, calculation of the vector images A and B may be explicitor implicit, and the two vector images may be weighted differently asdescribed herein.

The terms a or an, as used herein, are defined as one or more than one.The term plurality, as used herein, is defined as two or more than two.The term another, as used herein, is defined as at least a second ormore. The terms including and/or having, as used herein, are defined ascomprising (i.e., open language). The term coupled, as used herein, isdefined as connected, although not necessarily directly, and notnecessarily mechanically. The term program, computing device program,and/or software, as used herein, is defined as a sequence ofinstructions designed for execution on a computer system. A program mayinclude, for example, a subroutine, a function, a procedure, an objectmethod, an object implementation, and an executable application and/orother sequence of instructions designed for execution on a computersystem.

REFERENCES

The following references, and any reference mentioned in thisapplication, are herein incorporated by reference in full:

-   1. Ma J. MRM 2004; 52(2):415-419.-   2. Ma J, et al. JMRI 2006; 23(1):36-41.-   3. Xiang Q S. MRM 2006; 56(3):572-584.-   4. Eggers H, et al. ISMRM, 2010. p. 770.-   5. Eggers H. ISMRM 2010. p. 2924.-   6. Berglund et. al., Magnetic Resonance in Medicine 65:994-1004    (2011)-   7. U.S. Pat. No. 7,227,359-   8. U.S. Pat. No. 7,888,936-   9. Eggers H, et al., Magnetic Resonance in Medicine 65(1):96-107,    2011.

1. A computerized method for generating a phase corrected magneticresonance image or images comprising: (a) acquiring a magnetic resonanceimage or images containing background or error phase information; (b)calculating two vector images A and B using the acquired image or imagesso that a vector orientation by one of the two vector images at a pixelis substantially determined by the background or error phase at thepixel, and the vector orientation at the pixel by the other vector imageis substantially different from that determined by the background orerror phase at the pixel; (c) applying a sequenced region growing phasecorrection algorithm to the vector images A and B to construct a newvector image V, wherein the algorithm comprises: (i) selecting aninitial seed pixel or pixels and assigning either A or B of the initialseed pixel or pixels as a value of V for the initial seed pixel orpixels; (ii) selecting a secondary seed pixel and selecting either A orB of the secondary seed pixel as a value of V for the secondary seedpixel based on whether A or B of the secondary seed pixel has a smallerangular difference with an estimated V for the secondary seed pixel;(iii) determining for the secondary seed pixel a local quality metricfor each of the nearest neighbor pixels of the secondary seed pixel forwhich V has not been determined and assigning a priority to each of thenearest neighbor pixels using the local quality metric in order todetermine the sequence by which each of the nearest neighbor pixels isto be selected as a further seed pixel; (iv) repeating the steps of (ii)and (iii) to complete the sequenced region growing with respect tofurther seed pixels and to construct the vector image V so that a vectororientation of V at each pixel is substantially determined by thebackground or error phase at the pixel; (d) generating the phasecorrected magnetic resonance image or images from the acquired magneticresonance image or images using the vector image V; and (e) displayingor archiving the phase corrected magnetic resonance image or images. 2.The method of claim 1, further comprising correcting vector images A andB with a global linear error phase correction in one or more dimensionsprior to performing the sequenced region growing.
 3. The method of claim1, further comprising applying a low-pass filter to vector image Vbefore generating the phase corrected magnetic resonance image orimages.
 4. The method of claim 1, wherein amplitudes of the vectorimages A and B at a pixel are weighted by a signal amplitude at thepixel.
 5. The method of claim 1, wherein an initial seed pixel or pixelsare selected from a high-quality region, wherein high-quality comprisesa predetermined signal-to-noise ratio or a predetermined localorientational coherence for the vector images A or B.
 6. The method ofclaim 1, wherein an initial seed pixel or pixels and the value of V atthe initial seed pixel or pixels are selected based on an orientationalcoherence of either A or B at the initial seed pixel or pixels with V ata spatially or temporally neighboring pixel or pixels of a spatially ortemporally neighboring image for which V is already known or has beendetermined.
 7. The method of claim 1, wherein an initial seed pixel orpixels are placed onto a high priority pixel stack or stacks among aseries of pixel stacks that are initially empty and which facilitate asequencing of the sequenced region growing.
 8. The method of claim 1,wherein a pixel is selected as a secondary seed pixel if it has not beenprocessed previously as a seed pixel and it is on a pixel stack that hasa highest priority among pixel stacks that contain at least one pixelthat has not been processed as a seed pixel.
 9. The method of claim 1,wherein the local quality metric of a pixel is calculated as the smallerof two orientational differences between A and B of the pixel with anestimated V for the pixel.
 10. The method of claim 9, wherein theestimated V for a pixel is a first order estimation that includes anaverage and a linear expansion of V for pixels that are located within aneighboring region of the pixel and for which V has been previouslydetermined.
 11. The method of claim 9, wherein the estimated V for apixel is a zeroth order estimation calculated as an average of V forpixels located within a neighboring region of the pixel and for which Vhas been previously determined.
 12. The method of claim 11, wherein asize of the neighboring region is either fixed or adaptively adjustedbased on a local quality metric for the pixel.
 13. The method of claim11, wherein a size of the neighboring region is either fixed oradaptively adjusted based on a local quality metric for the pixel. 14.The method of claim 1, wherein the maximum possible range of 0-π for theangular difference between any two vectors is used to gauge and bin thelocal quality metric and to place a pixel onto a pixel stack.
 15. Themethod of claim 14, wherein the pixel stack covering a subrange of 0-πfor the quality metric is assigned a priority, and wherein a pixel stackof a higher priority is for receiving pixels with a smaller qualitymetric and a pixel stack of a lower priority is for receiving pixelswith a larger quality metric.
 16. The method of claim 15, wherein thepriority of a pixel stack from which a pixel is selected as a seed pixelis recorded for the sequenced region growing as a quality metric indexto reflect an integrity of the sequenced region growing.
 17. The methodof claim 16, wherein the quality metric index is used to segment animage into different segments of possible inconsistent region growingand then to combine the different segments into an overall consistentregion growing to form a final vector image V.
 18. The method of claim1, wherein a value of the vector A for an initial seed pixel is assignedas V_(A), and a sequenced region growing is performed to construct avector image V_(A), and wherein a value of the vector B for the sameinitial seed pixel is assigned as V_(B), and another sequenced regiongrowing is performed to construct a vector image V_(B).
 19. The methodof claim 18, wherein either vector image V_(A) or vector image V_(B) isset to be a final vector image V, depending on whether vector imageV_(A) or vector image V_(B) has a greater overall orientationalsmoothness.
 20. The method of claim 1, wherein the sequenced regiongrowing is performed in two spatial dimensions.
 21. The method of claim1, wherein the sequenced region growing is performed in three spatialdimensions.
 22. The method of claim 1, wherein the sequenced regiongrowing is performed by including the temporal dimension for a series ofdynamically acquired images.
 23. The method of claim 1 wherein acquiringa magnetic resonance image or images comprises acquiring two-point Dixonwater and fat images, wherein a first image S1 is acquired at a firstecho time TE1 and a second image S2 is acquired at a second echo timeTE2.
 24. The method of claim 23, wherein acquiring two-point Dixon waterand fat images comprises using dual-echo bipolar readout gradients. 25.The method of claim 23, wherein acquiring two-point Dixon water and fatimages comprises using dual-echo unipolar readout gradients.
 26. Themethod of claim 23, wherein acquiring two-point Dixon water and fatimages comprises using triple-echo readout gradients.
 27. The method ofclaim 23, wherein acquiring two-point Dixon water and fat imagescomprises using interleaved single echo readout gradients.
 28. Themethod of claim 23, wherein selection of TE1 and TE2 is flexible exceptto avoid a small orientational difference between vector image A andvector image B.
 29. The method of claim 23, wherein the images S₁ and S₂are expressed according to the following equations:S ₁=(W+δ ₁ Fe ^(iθ) ¹ )P ₁S ₂=(W+δ ₂ Fe ^(iθ) ² )P ₁ P where W and F are amplitudes for water andfat respectively, P₁ is a phase factor of image S₁, P is an additionalphase factor of image S₂ relative to image S₁ and is determined by abackground or error phase, and the method further comprises determiningby an image based pre-calibration an amplitude attenuation factor (δ₁,δ₂) and phase (θ₁, θ₂) as a function of two echo times (TE1, TE2) forthe fat signal.
 30. The method of claim 29, wherein pre-calibration of(δ₁, δ₂) is performed in part by determining an echo time dependence ofa signal amplitude of a known fat-only image region, and pre-calibrationof (θ₁, θ₂) is performed in part by determining an echo time dependenceof a phase discontinuity between a known fat-only image region and aneighboring known water-only region.
 31. The method of claim 29, whereinpre-calibration is performed for a given pulse sequence, a scanprotocol, or a field strength.
 32. The method of claim 23, wherein theimages S₁ and S₂ are used to generate two vector images A and B asexpressed according to the following equations:A=S* ₁ S ₂ [Q _(A)+δ₁(1−Q _(A))e ^(iθ) ¹ ][Q _(A)+δ₂(1−Q _(A))e ^(−iθ) ²]B=S* ₁ S ₂ [Q _(B)+δ₁(1−Q _(B))e ^(iθ) ¹ ][Q _(B)+δ₂(1−Q _(B))e ^(−iθ) ²] where Q_(A) and Q_(B) are the two mathematically possible solutions ofthe following quadratic equation of Q, which is defined as$Q = \frac{W}{W + F}$ (i.e., the water fraction for a given pixel):[(1+δ₂ ²−2δ₂ cos θ₂)M ₁−(1+δ₁ ²−2δ₁ cos θ₁)M ₂ ]Q ²−2[(δ₂ ²−δ₂ cos θ₂)M₁−(δ₁ ²−δ₁ cos θ₁)M ₂ ]Q+[(M ₁δ₂ ² −M ₂δ₁ ²)]=0 where M₁ and M₂ are thesquare of the amplitudes of the images S₁ and S₂, respectively (i.e.,M₁=|S₁|² and M₂=|S₂|²).
 33. The method of claim 32, wherein the vectorimages are further normalized and weighted by a signal amplitude, suchas: $A^{\prime} = {\frac{A}{A}\sqrt{M_{1} + M_{2}}}$$B^{\prime} = {\frac{B}{B}\sqrt{M_{1} + M_{2}}}$ where again,M₁=|S₁|² and M₂=|S₂|².
 34. The method of claim 33, wherein sequencedregion growing is used to construct a vector image V from the two vectorimages A and B.
 35. The method of claim 34, wherein the vector image Vis used to phase correct and remove the phase factor P from the imageS₂, the phase corrected S₂ is combined with S₁ to solve for WP₁ and FP₁,and then to generate a water-only image and a fat-only image accordingto the following equations:W=Real{(WP ₁) WP ₁ */| WP ₁ |}F=Real{(FP ₁) FP ₁ */| FP ₁ |} where Real{ . . . } is to take the realcomponent of its complex argument, * is to take the complex conjugate ofits argument, and WP₁ and FP₁ represent low-pass filtering of WP₁ andFP₁, respectively.
 36. The method of claim 1 wherein acquiring amagnetic resonance image or images comprises acquiring a single-pointDixon water and fat image wherein a flexible echo time TE is used andthe acquired magnetic resonance image is expressed as: S=(W+Fe^(iθ))P,where θ is dependent on TE and the dependence is determined with animage-based pre-calibration, and P(≡e^(iφ)) is a phase factor for theimage S.
 37. The method of claim 36, wherein the vector image A is setto S and the vector image B is set to Se^(−iθ).
 38. The method of claim37, wherein a sequenced region growing is used to construct a vectorimage V from the two vector images A and B, the vector image V is usedto phase correct or remove P from S to form S′, and a water-only imageand a fat-only image are generated according to:F=Imag{S′}/sin θW=Real{S′F cos θ} where Real{ . . . } and Imag{ . . . } are to take thereal and imaginary components of their component, respectively.
 39. Themethod of claim 1, wherein acquiring a magnetic resonance image orimages comprises acquiring a single-point silicone specific imagewherein an echo time TE when water and fat signals are substantiallyin-phase is used, and the acquired magnetic resonance image is expressedaccording to the following equation:S=(W+F+Ie ^(iθ))P where θ is determined with an image-basedpre-calibration for the echo time TE as a phase discontinuity of a knownsilicone-only image region and a neighboring known water or fat onlyimage region, and P(≡e^(iφ)) is a phase factor for the image S.
 40. Themethod of claim 39, wherein vector image A is set to S and vector imageB is set to Se^(−iθ).
 41. The method of claim 40, wherein a sequencedregion growing is used to construct a vector image V from the two vectorimages A and B, the vector image V is used to phase correct or remove Pfrom S to form S′, and a silicone-only image and a silicone-suppressedimage are generated according to:I=Imag{S′}/sin θW+F=Real{S′−I cos θ} where Real{ . . . } and Imag{ . . . } are to takethe real and imaginary components of their component, respectively. 42.The method of claim 1, wherein acquiring a magnetic resonance image orimages comprises acquiring an inversion recovery image at an inversionrecovery time TI and the image is expressed according to the followingequation:S=Ie ^(iθ) where I is a signal magnitude and θ is a measured signalphase that comprises a background or error phase and an intrinsic signalphase.
 43. The method of claim 42, wherein vector image A is set to Sand vector image B is set to −S.
 44. The method of claim 43, wherein asequenced region growing is used to construct a vector image V from thetwo vector images A and B, the vector image V is used to phase correctthe image S, and the phase corrected image S is displayed and archivedas a phase sensitive inversion recovery image.
 45. A system forgenerating a phase corrected magnetic resonance image or imagescomprising: (A) a magnetic resonance imaging controller; (B) a processorcoupled to the controller and configured to execute phase correctioninstructions applicable to a magnetic resonance image or images, whereinthe instructions comprise: (a) calculating two vector images A and Bassociated with an acquired image or images so that a vector orientationby one of the two vector images at a pixel is substantially determinedby a background or error phase at the pixel, and the vector orientationat the pixel by the other vector image is substantially different fromthat determined by the background or error phase at the pixel; (b)applying a sequenced region growing phase correction algorithm to thevector images A and B to construct a new vector image V, wherein thesequenced region growing phase correction algorithm comprises: (i)selecting an initial seed pixel or pixels and assigning either A or B ofthe initial seed pixel or pixels as a value of V for the initial seedpixel or pixels; (ii) selecting a secondary seed pixel and selectingeither A or B of the secondary seed pixel as a value of V for thesecondary seed pixel based on whether A or B of the secondary seed pixelhas a smaller angular difference with an estimated V for the secondaryseed pixel; (iii) determining for the secondary seed pixel a localquality metric for each of the nearest neighbor pixels of the secondaryseed pixel for which V has not been determined and assigning a priorityto each of the nearest neighbor pixels using the local quality metric inorder to determine the sequence by which each of the nearest neighborpixels is to be selected as a further seed pixel; (iv) repeating thesteps of (ii) and (iii) to complete the sequenced region growing withrespect to further seed pixels and to construct the vector image V sothat a vector orientation of V at each pixel is substantially determinedby the background or error phase at the pixel; (c) generating a phasecorrected magnetic resonance image or images from the acquired magneticresonance image or images using the vector image V; and (d) displayingor archiving the phase corrected magnetic resonance image or images; and(C) an output or storage device configured to display or store the phasecorrected magnetic resonance image or images.
 46. The system of claim45, wherein the processor is further configured to execute phasecorrection instructions reflecting the method of claim
 2. 47. The systemof claim 46, wherein the processor is further configured to executephase correction instructions reflecting the method of claim
 3. 48. Thesystem of claim 46, wherein the processor is further configured toexecute phase correction instructions reflecting the method of claim 4.49. The system of claim 46, wherein the processor is further configuredto execute phase correction instructions reflecting the method of claim5.
 50. The system of claim 46, wherein the processor is furtherconfigured to execute phase correction instructions reflecting themethod of claim
 6. 51. The system of claim 46, wherein the processor isfurther configured to execute phase correction instructions reflectingthe method of claim
 7. 52. The system of claim 46, wherein the processoris further configured to execute phase correction instructionsreflecting the method of claim
 8. 53. The system of claim 46, whereinthe processor is further configured to execute phase correctioninstructions reflecting the method of claim
 9. 54. The system of claim46, wherein the processor is further configured to execute phasecorrection instructions reflecting the method of claim
 10. 55. Thesystem of claim 46, wherein the processor is further configured toexecute phase correction instructions reflecting the method of claim 11.56. The system of claim 46, wherein the processor is further configuredto execute phase correction instructions reflecting the method of claim12.
 57. The system of claim 46, wherein the processor is furtherconfigured to execute phase correction instructions reflecting themethod of claim
 13. 58. The system of claim 46, wherein the processor isfurther configured to execute phase correction instructions reflectingthe method of claim
 14. 59. The system of claim 46, wherein theprocessor is further configured to execute phase correction instructionsreflecting the method of claim
 15. 60. The system of claim 46, whereinthe processor is further configured to execute phase correctioninstructions reflecting the method of claim
 16. 61. The system of claim46, wherein the processor is further configured to execute phasecorrection instructions reflecting the method of claim
 17. 62. Thesystem of claim 46, wherein the processor is further configured toexecute phase correction instructions reflecting the method of claim 18.63. The system of claim 46, wherein the processor is further configuredto execute phase correction instructions reflecting the method of claim19.
 64. The system of claim 46, wherein the processor is furtherconfigured to execute phase correction instructions reflecting themethod of claim
 20. 65. The system of claim 46, wherein the processor isfurther configured to execute phase correction instructions reflectingthe method of claim
 21. 66. The system of claim 46, wherein theprocessor is further configured to execute phase correction instructionsreflecting the method of claim
 22. 67. The system of claim 46, whereinthe processor is further configured to execute phase correctioninstructions reflecting the method of claim
 23. 68. The system of claim46, wherein the processor is further configured to execute phasecorrection instructions reflecting the method of claim
 24. 69. Thesystem of claim 46, wherein the processor is further configured toexecute phase correction instructions reflecting the method of claim 25.70. The system of claim 46, wherein the processor is further configuredto execute phase correction instructions reflecting the method of claim26.
 71. The system of claim 46, wherein the processor is furtherconfigured to execute phase correction instructions reflecting themethod of claim
 27. 72. The system of claim 46, wherein the processor isfurther configured to execute phase correction instructions reflectingthe method of claim
 28. 73. The system of claim 46, wherein theprocessor is further configured to execute phase correction instructionsreflecting the method of claim
 29. 74. The system of claim 46, whereinthe processor is further configured to execute phase correctioninstructions reflecting the method of claim
 30. 75. The system of claim46, wherein the processor is further configured to execute phasecorrection instructions reflecting the method of claim
 31. 76. Thesystem of claim 46, wherein the processor is further configured toexecute phase correction instructions reflecting the method of claim 32.77. The system of claim 46, wherein the processor is further configuredto execute phase correction instructions reflecting the method of claim33.
 78. The system of claim 46, wherein the processor is furtherconfigured to execute phase correction instructions reflecting themethod of claim
 34. 79. The system of claim 46, wherein the processor isfurther configured to execute phase correction instructions reflectingthe method of claim
 35. 80. The system of claim 46, wherein theprocessor is further configured to execute phase correction instructionsreflecting the method of claim
 36. 81. The system of claim 46, whereinthe processor is further configured to execute phase correctioninstructions reflecting the method of claim
 37. 82. The system of claim46, wherein the processor is further configured to execute phasecorrection instructions reflecting the method of claim
 39. 83. Thesystem of claim 46, wherein the processor is further configured toexecute phase correction instructions reflecting the method of claim 40.84. The system of claim 46, wherein the processor is further configuredto execute phase correction instructions reflecting the method of claim41.
 85. The system of claim 46, wherein the processor is furtherconfigured to execute phase correction instructions reflecting themethod of claim
 42. 86. The system of claim 46, wherein the processor isfurther configured to execute phase correction instructions reflectingthe method of claim
 43. 87. The system of claim 46, wherein theprocessor is further configured to execute phase correction instructionsreflecting the method of claim
 44. 88. A non-transitory computerreadable storage medium with an executable program stored thereon,wherein the program instructs a microprocessor to perform stepscomprising: (a) loading into memory a magnetic resonance image orimages; (b) calculating two vector images A and B associated with theloaded image or images so that a vector orientation by one of the twovector images at a pixel is substantially determined by a background orerror phase at the pixel, and the vector orientation at the pixel by theother vector image is substantially different from that determined bythe background or error phase at the pixel; (c) applying a sequencedregion growing phase correction algorithm to the vector images A and Bto construct a new vector image V, wherein the sequenced region growingphase correction algorithm comprises: (i) selecting an initial seedpixel or pixels and assigning either A or B of the initial seed pixel orpixels as a value of V for the initial seed pixel or pixels; (ii)selecting a secondary seed pixel and selecting either A or B of thesecondary seed pixel as a value of V for the secondary seed pixel basedon whether A or B of the secondary seed pixel has a smaller angulardifference with an estimated V for the secondary seed pixel; (iii)determining for the secondary seed pixel a local quality metric for eachof the nearest neighbor pixels of the secondary seed pixel for which Vhas not been determined and assigning a priority to each of the nearestneighbor pixels using the local quality metric to determine the sequenceby which each of the nearest neighbor pixels is to be selected as afurther seed pixel; (iv) repeating the steps of (ii) and (iii) tocomplete the sequenced region growing with respect to further seedpixels and to construct the vector image V so that a vector orientationof V at each pixel is substantially determined by the background orerror phase at the pixel; (d) generating the phase corrected magneticresonance image or images from the acquired magnetic resonance image orimages using the vector image V; and (e) displaying or archiving thephase corrected magnetic resonance image or images.
 89. Thenon-transitory computer readable storage medium of claim 88, with anexecutable program stored thereon, wherein the program further instructsa microprocessor to perform steps reflecting the method of claim
 2. 90.The non-transitory computer readable storage medium of claim 88, with anexecutable program stored thereon, wherein the program further instructsa microprocessor to perform steps reflecting the method of claim
 3. 91.The non-transitory computer readable storage medium of claim 88, with anexecutable program stored thereon, wherein the program further instructsa microprocessor to perform steps reflecting the method of claim
 4. 92.The non-transitory computer readable storage medium of claim 88, with anexecutable program stored thereon, wherein the program further instructsa microprocessor to perform steps reflecting the method of claim
 5. 93.The non-transitory computer readable storage medium of claim 88, with anexecutable program stored thereon, wherein the program further instructsa microprocessor to perform steps reflecting the method of claim
 6. 94.The non-transitory computer readable storage medium of claim 88, with anexecutable program stored thereon, wherein the program further instructsa microprocessor to perform steps reflecting the method of claim
 7. 95.The non-transitory computer readable storage medium of claim 88, with anexecutable program stored thereon, wherein the program further instructsa microprocessor to perform steps reflecting the method of claim
 8. 96.The non-transitory computer readable storage medium of claim 88, with anexecutable program stored thereon, wherein the program further instructsa microprocessor to perform steps reflecting the method of claim
 9. 97.The non-transitory computer readable storage medium of claim 88, with anexecutable program stored thereon, wherein the program further instructsa microprocessor to perform steps reflecting the method of claim
 10. 98.The non-transitory computer readable storage medium of claim 88, with anexecutable program stored thereon, wherein the program further instructsa microprocessor to perform steps reflecting the method of claim
 11. 99.The non-transitory computer readable storage medium of claim 88, with anexecutable program stored thereon, wherein the program further instructsa microprocessor to perform steps reflecting the method of claim 12.100. The non-transitory computer readable storage medium of claim 88,with an executable program stored thereon, wherein the program furtherinstructs a microprocessor to perform steps reflecting the method ofclaim
 13. 101. The non-transitory computer readable storage medium ofclaim 88, with an executable program stored thereon, wherein the programfurther instructs a microprocessor to perform steps reflecting themethod of claim
 14. 102. The non-transitory computer readable storagemedium of claim 88, with an executable program stored thereon, whereinthe program further instructs a microprocessor to perform stepsreflecting the method of claim
 15. 103. The non-transitory computerreadable storage medium of claim 88, with an executable program storedthereon, wherein the program further instructs a microprocessor toperform steps reflecting the method of claim
 16. 104. The non-transitorycomputer readable storage medium of claim 88, with an executable programstored thereon, wherein the program further instructs a microprocessorto perform steps reflecting the method of claim
 17. 105. Thenon-transitory computer readable storage medium of claim 88, with anexecutable program stored thereon, wherein the program further instructsa microprocessor to perform steps reflecting the method of claim 18.106. The non-transitory computer readable storage medium of claim 88,with an executable program stored thereon, wherein the program furtherinstructs a microprocessor to perform steps reflecting the method ofclaim
 19. 107. The non-transitory computer readable storage medium ofclaim 88, with an executable program stored thereon, wherein the programfurther instructs a microprocessor to perform steps reflecting themethod of claim
 20. 108. The non-transitory computer readable storagemedium of claim 88, with an executable program stored thereon, whereinthe program further instructs a microprocessor to perform stepsreflecting the method of claim
 21. 109. The non-transitory computerreadable storage medium of claim 88, with an executable program storedthereon, wherein the program further instructs a microprocessor toperform steps reflecting the method of claim
 22. 110. The non-transitorycomputer readable storage medium of claim 88, with an executable programstored thereon, wherein the program further instructs a microprocessorto perform steps reflecting the method of claim
 23. 111. Thenon-transitory computer readable storage medium of claim 88, with anexecutable program stored thereon, wherein the program further instructsa microprocessor to perform steps reflecting the method of claim 24.112. The non-transitory computer readable storage medium of claim 88,with an executable program stored thereon, wherein the program furtherinstructs a microprocessor to perform steps reflecting the method ofclaim
 25. 113. The non-transitory computer readable storage medium ofclaim 88, with an executable program stored thereon, wherein the programfurther instructs a microprocessor to perform steps reflecting themethod of claim
 26. 114. The non-transitory computer readable storagemedium of claim 88, with an executable program stored thereon, whereinthe program further instructs a microprocessor to perform stepsreflecting the method of claim
 27. 115. The non-transitory computerreadable storage medium of claim 88, with an executable program storedthereon, wherein the program further instructs a microprocessor toperform steps reflecting the method of claim
 28. 116. The non-transitorycomputer readable storage medium of claim 88, with an executable programstored thereon, wherein the program further instructs a microprocessorto perform steps reflecting the method of claim
 29. 117. Thenon-transitory computer readable storage medium of claim 88, with anexecutable program stored thereon, wherein the program further instructsa microprocessor to perform steps reflecting the method of claim 30.118. The non-transitory computer readable storage medium of claim 88,with an executable program stored thereon, wherein the program furtherinstructs a microprocessor to perform steps reflecting the method ofclaim
 31. 119. The non-transitory computer readable storage medium ofclaim 88, with an executable program stored thereon, wherein the programfurther instructs a microprocessor to perform steps reflecting themethod of claim
 32. 120. The non-transitory computer readable storagemedium of claim 88, with an executable program stored thereon, whereinthe program further instructs a microprocessor to perform stepsreflecting the method of claim
 33. 121. The non-transitory computerreadable storage medium of claim 88, with an executable program storedthereon, wherein the program further instructs a microprocessor toperform steps reflecting the method of claim
 34. 122. The non-transitorycomputer readable storage medium of claim 88, with an executable programstored thereon, wherein the program further instructs a microprocessorto perform steps reflecting the method of claim
 35. 123. Thenon-transitory computer readable storage medium of claim 88, with anexecutable program stored thereon, wherein the program further instructsa microprocessor to perform steps reflecting the method of claim 36.124. The non-transitory computer readable storage medium of claim 88,with an executable program stored thereon, wherein the program furtherinstructs a microprocessor to perform steps reflecting the method ofclaim
 37. 125. The non-transitory computer readable storage medium ofclaim 88, with an executable program stored thereon, wherein the programfurther instructs a microprocessor to perform steps reflecting themethod of claim
 39. 126. The non-transitory computer readable storagemedium of claim 88, with an executable program stored thereon, whereinthe program further instructs a microprocessor to perform stepsreflecting the method of claim
 40. 127. The non-transitory computerreadable storage medium of claim 88, with an executable program storedthereon, wherein the program further instructs a microprocessor toperform steps reflecting the method of claim
 41. 128. The non-transitorycomputer readable storage medium of claim 88, with an executable programstored thereon, wherein the program further instructs a microprocessorto perform steps reflecting the method of claim
 42. 129. Thenon-transitory computer readable storage medium of claim 88, with anexecutable program stored thereon, wherein the program further instructsa microprocessor to perform steps reflecting the method of claim 43.130. The non-transitory computer readable storage medium of claim 88,with an executable program stored thereon, wherein the program furtherinstructs a microprocessor to perform steps reflecting the method ofclaim 44.